EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
2.
1.
Jake wanted to measure the width of
the pond, so he drew this diagram of
two similar triangles.
Pond
7 ft
If the side measurement of this cube is
tripled, what is the ratio of the surface
area of the original cube to the surface
area of the larger one?
18 ft
A
1:3
B
1:6
What is the approximate width, w, of
the pond?
C
1:9
A
25 feet
D
1:12
B
19 feet
C
18 feet
D
13 feet
3.
Page 1
w
5 ft
What is the measure of the larger of
two complementary angles if the
measure of one angle is five times
the measure of the other angle?
A
15°
B
16°
C
74°
D
75°
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
4.
John’s triangular sail has an area of
25 square feet. The sail’s height is
10 feet.
5.
4 feet radius
15 feet high
h = 10 ft
What is the approximate volume of
the water tank to the nearest whole
number?
A = 25 ft 2
A
189 cubic feet
B
377 cubic feet
C
754 cubic feet
D
1,508 cubic feet
b = ? ft
What is the length of the
base of the sail?
Page 2
A
2.5 ft
B
5 ft
C
15 ft
D
35 ft
6.
Garrett made a toy box for his younger
sister. The inside of the entire toy
box, including the lid, is 15 in. wide,
30 in. long, and 12 in. tall. Garrett
wants to line the inside, including the
lid, with purple cloth. How many
square feet of cloth should he buy?
A
3.125 ft2
B
8.125 ft2
C
13.75 ft 2
D
28.5 ft 2
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
7.
Mr. Gellar needs to paint the shaded part of the water tower.
18 ft
28 ft
20 ft
Water Tower
If a gallon of paint will cover 200 square feet, what is the least number of gallons of paint
needed to complete the job?
8.
A
5
B
6
C
7
D
8
Jaden’s new toy chest is in the shape
of a rectangular pyramid. The
dimensions of the base are 3 ft 9 in.
and 4 ft 6 in. The height is 4 ft 3 in.
What is the approximate volume of
the pyramid?
A
B
Page 3
23.9 ft
9.
What is the approximate volume of a
cone with a radius of 6 inches and a
height of 9 inches?
A
113.04 in.3
B
339.29 in.3
C
1017.88 in.3
D
1356.48 in.3
3
25.7 ft3
C
35.9 ft3
D
38.6 ft3
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
10.
Rae built a gate for her backyard. The
height of the gate is 3 feet and the
width is 5 feet. About how long is its
support piece that goes along the
diagonal?
A
34 ft
B
8 ft
C
6 ft
D
3 ft
12.
A ladder leans against the side of a
building. The base of the ladder is
5 meters from the building, and the
top is 12 meters above the ground.
12 m
11.
Jamie and Fred are meeting Sarita at
her house. Jamie must use the
crosswalk in front of Fred’s house to
cross the street.
5m
What is the length of the ladder?
Sarita’s
House
112 ft
Jamie’s
House
A
11 meters
B
13 meters
C
17 meters
D
169 meters
Fred’s
House
What is the total distance Jamie must
walk?
Page 4
A
66 ft
B
130 ft
C
178 ft
D
199 ft
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
13.
A square pyramid has a volume of
32 cubic units. What would be the
volume if the dimensions of the
square base were doubled?
A
The volume would be two times
the original.
15.
Juan built a square pyramid in the
sand. He built a second pyramid
with the same size base that was
one third as tall as the first one.
What would be the volume of the
second pyramid?
A
B
The volume would be three times
the original.
C
The volume would be four times
the original.
B
The volume would be eight times
the original.
C
The volume would be 3 times as
much as the first pyramid.
D
The volume would be 9 times as
much as the first pyramid.
D
14.
Page 5
The volume would be 19 as much as
If the height of a cylinder was tripled,
but the area of the base remained the
same, what would happen to the
volume?
A
The volume would double.
B
The volume would triple.
C
The volume would be four times
greater.
D
The volume would be nine times
greater.
the first pyramid.
The volume would be 13 as much as
the first pyramid.
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
16.
The diagram below shows a company’s
current packaging of its plant food.
17.
7 cm
10 cm
If the company doubles the radius of
its current packaging, what effect will
this change have on the volume of the
container?
A
18.
At noon, the shadow of a flagpole is
19 feet long. At the same time, the
shadow of a 12-foot wall is 4 feet long.
What is the height of the flagpole?
A
48 feet
B
57 feet
C
62 feet
D
75 feet
D ABC @ D DEF with a right angle
at B and –C = 42 ∞ .
The volume will be one and a half
times the original packaging
volume.
E
B
D
B
C
D
Page 6
The volume will be twice the
original packaging volume.
The volume will be three times
the original packaging volume.
The volume will be four times the
original packaging volume.
A
F
C
What is the measure of – D?
A
42°
B
48°
C
58°
D
90°
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
19.
20.
A copying machine reduces a 12-inch line segment to 10.5 inches. At this setting, what
would a 16-inch line segment become?
A
12 inches
B
14 inches
C
16 inches
D
18 inches
If WXYZ were rotated 180° about point Z, what would be the coordinates of point Y' ?
y
(0,4) W
X (5,4)
(0,1) Z
Y (5,1)
x
Page 7
A
(—5, 1)
B
(5, 1)
C
(—5, —1)
D
(5, —1)
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
21.
If triangle ABC were rotated 90° counterclockwise about the origin, what would be
the coordinates of B′ ?
y
+6
+5
+4
C
+3
+2
+1
—6 — 5 — 4 — 3 —2 —1 0
—1
A
B
+1 +2 +3 +4 +5 +6
x
—2
—3
—4
—5
—6
Page 8
A
(4,1)
B
(0,4)
C
( —1, —4)
D
( —1,4)
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
1
22. Given D DEF, which figure illustrates a dilation with a scale factor of 2 ?
y
F
D
E
x
0
y
A
y
B
F′
F′
D′
D′
E′
x
0
y
C
E′
x
0
y
D
F′
D′
D′
E′
0
x
x
0
E′
Page 9
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
F′
EOG Mathematics Grade 8 Sample Items Goal 2
North Carolina Testing Program
y
23. If quadrilateral ABCD is dilated
with a scale factor of 3, which of
the following would be the result?
+
12
+
11
+
9
+
8
+
7
+
6
+
5
+
4
+
3
+
2
+
1
D
—
10
+
—
—
—
—
—
—
—
—
—
12 — 11 — 10 9 8 7 6 5 4 3
2 1 0
—
1
A
—
—
2
—
3
—
4
—
5
—
6
—
7
—
8
—
9
C
+
1
y
+
+
+
11
—
12
y
11
10
9
8
+
8
+
7
+
7
+
6
+
6
5
9
5
+
+
4
+
4
+
3
+
3
+
2
+
2
1
+
1
—
2
—
—
—
—
+
1
+
2
+
+
3
4
+
5
+
6
+
7 + 8 + 9 + 10 + 11 + 12
x
—
B´
A´
—
2
3
—
3
4
—
4
5
—
5
—
6
—
6
—
7
—
7
—
8
—
8
9
—
9
10
—
10
11
—
11
—
12
—
12
+
12
+
12
+
11
+
11
+
10
+
D´
9
9
8
8
7
+
7
+
6
+
6
+
5
+
5
4
4
+
+
3
+
3
+
2
+
2
+
1
+
1
—
2
—
3
—
4
—
—
—
+
1
+
2
+
3
+
4
+
5
+
6
+
7 + 8 + 9 + 10 + 11 + 12
x
—
—
—
—
—
—
—
—
—
—
12 — 11 — 10 9 8 7 6 5 4 3 2 1 0
—
1
—
2
—
3
—
4
5
—
5
6
—
6
7
—
7
—
8
—
8
—
9
—
9
—
10
—
—
+
1
+
2
+
3
+
4
+
5
+
6
+
7 + 8 + 9 + 10 + 11 + 12
+
4
+
5
+
6
+
7 + 8 + 9 + 10 + 11 + 12
x
B´
10
+
+
—
—
—
—
—
—
—
—
—
12 — 11 — 10 9 8 7 6 5 4 3 2 1 0
—
1
C´
y
D
+
+
D´
—
—
—
—
—
—
—
—
—
12 — 11 — 10 9 8 7 6 5 4 3 2 1 0
—
1
—
+
x
7 + 8 + 9 + 10 + 11 + 12
12
+
C´
+
(3x, 3y)
+
+
Page 10
6
10
—
B
y
A´
+
5
+
—
—
+
+
A´
C´
4
10
—
—
—
—
—
—
—
—
—
12 — 11 — 10 9 8 7 6 5 4 3 2 1 0
—
1
D´
+
11
+
C
3
+
+
—
+
12
+
D´
2
B
(x, y)
A
+
B´
A´
—
10
11
—
11
12
—
12
C´
+
1
+
2
+
3
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
B´
x
North Carolina Testing Program
EOG Mathematics Grade 8 Sample Items Goal 2
For a classroom assignment, Ashley needs to estimate the mass of her cheese sandwich.
Which would be the most reasonable estimate?
24.
A
200 grams
B
3 kilograms
C
27 centigrams
D
300 milligrams
End of Goal 2 Sample Items
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Page 11
Published November 2003. May reproduce for instructional and
educational purposes only; not for personal or financial gain.
Answers to EOG Mathematics Grade 8 Sample Items
Goal 2
1.
Objective 2.01
Use geometric concepts and modeling to interpret and solve problems.
Thinking Skill: Applying
Correct Answer: C
2.
Objective 2.01
Use geometric concepts and modeling to interpret and solve problems.
Thinking Skill: Integrating
Correct Answer: D
3.
Objective 2.01
Use geometric concepts and modeling to interpret and solve problems.
Thinking Skill: Applying
Correct Answer: D
4.
Objective 2.01
Use geometric concepts and modeling to interpret and solve problems.
Thinking Skill: Applying
Correct Answer: B
5.
Objective 2.01
Use geometric concepts and modeling to interpret and solve problems.
Thinking Skill: Applying
Correct Answer: C
6.
Objective 2.03
Find the surface area of rectangular solids and cylinders.
Thinking Skill: Integrating
Correct Answer:
C
Objective 2.03
Find the surface area of rectangular solids and cylinders.
Thinking Skill: Integrating
Correct Answer:
B
7.
8.
Objective 2.05
Find the volume of prisms, cylinders, pyramids, and cones, with and without
models.
Thinking Skill: Applying
Correct Answer: A
9.
Objective 2.05
Find the volume of prisms, cylinders, pyramids, and cones, with and without
models.
Thinking Skill: Applying
Correct Answer: B
10. Objective 2.06
Use the Pythagorean Theorem to solve problems.
Thinking Skill: Applying
Correct Answer:
North Carolina Testing Program
C
Published November 2003. May reproduce for instructional and educational
purposes only; not for personal or financial gain.
Answers to EOG Mathematics Grade 8 Sample Items
Goal 2
11.
Objective 2.06
Use the Pythagorean Theorem to solve problems.
Thinking Skill: Applying
Correct Answer:
C
12. Objective 2.06
Use the Pythagorean Theorem to solve problems.
Thinking Skill: Applying
Correct Answer:
B
13. Objective 2.07
Determine the effect on the volume of solid figures when one or more
dimension is changed.
Thinking Skill: Analyzing
Correct Answer: C
14. Objective 2.07
Determine the effect on the volume of solid figures when one or more
dimension is changed.
Thinking Skill: Analyzing
Correct Answer: B
15. Objective 2.07
Determine the effect on the volume of solid figures when one or more
dimension is changed.
Thinking Skill: Analyzing
Correct Answer: B
16. Objective 2.07
Determine the effect on the volume of solid figures when one or more
dimension is changed.
Thinking Skill: Analyzing
Correct Answer: D
17. Objective 2.08
Solve problems related to similar and congruent figures.
Thinking Skill: Applying
Correct Answer:
B
18. Objective 2.08
Solve problems related to similar and congruent figures.
Thinking Skill: Applying
Correct Answer:
B
19. Objective 2.08
Solve problems related to similar and congruent figures.
Thinking Skill: Applying
Correct Answer:
B
North Carolina Testing Program
Published November 2003. May reproduce for instructional and educational
purposes only; not for personal or financial gain.
Answers to EOG Mathematics Grade 8 Sample Items
Goal 2
20. Objective 2.09
Locate, give the coordinates of, and graph plane figures which are the
results of rotations (multiples of 90 degrees). Graph plane figures which
are similar to a given figure (dilations).
Thinking Skill: Analyzing
Correct Answer: A
21. Objective 2.09
Locate, give the coordinates of, and graph plane figures which are the
results of rotations (multiples of 90 degrees). Graph plane figures which
are similar to a given figure (dilations).
Thinking Skill: Analyzing
Correct Answer: D
22. Objective 2.09
Locate, give the coordinates of, and graph plane figures which are the
results of rotations (multiples of 90 degrees). Graph plane figures which
are similar to a given figure (dilations).
Thinking Skill: Analyzing
Correct Answer: A
23. Objective 2.09
Locate, give the coordinates of, and graph plane figures which are the
results of rotations (multiples of 90 degrees). Graph plane figures which
are similar to a given figure (dilations).
Thinking Skill: Analyzing
Correct Answer: D
24. Objective 2.12
Select appropriate units and tools for measurement tasks within problemsolving situations; determine precision; check for reasonableness of results.
Thinking Skill: Analyzing
Correct Answer: A
North Carolina Testing Program
Published November 2003. May reproduce for instructional and educational
purposes only; not for personal or financial gain.